IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. AP-30, NO.

6 , NOVEMBER 1982

1237

Radiation from Aperture Antennas Radiating the in Presence of a Dielectric Sphere M. S . NARASIMHAN, SENIOR MEMBER, IEEE AND
S . RAVISHANKAR, STUDENT MEMBER, IEEE
Absrract-A more systematic and rigorous procedure for analyzing the radiation patterns of an open-ended Waveguide radiating in the presence of a dielectric sphere is presented. The analysisis based on the formula developed earlier [5] for radial translation of the sphericalvectorwavefunctions. An experimentalprogram is described which confirms the validity of the analysis presented.

tx

Fig. 1. Coordinate system for analysis of radiation patterns.

I. INTRODUCTION The radiation characteristics of a dielectric sphere mounted infront of anopen-endeddominantmode waveguidehave received considerable attention inthe past [ 1 ] -[ 31. This study is ofsignificance in multiple- or adaptive-beam parabolic antennas, dielectric in heating, and in beam switching using dielectric lenses. This problem is also of significance in studies on interaction of microwaves with biological objects modeled asdielectricspheres [4]. However, no systematicapproach was presented in the past t o analyze radiation characteristics of aperture antennas, radiating in the presence of a dielectric sphere. The techniques presented in the past involved approximating the aperture antenna to be a combination of electric and magnetic Hertzian dipoles [ 1I , [ 21 o r taking recourse t o "ray tracing" procedure whenever the radiating aperture exhibited rotational symmetry[3 J . Inthiscommunication,suchapproximationsareavoided and the radiating near fields of the open-ended waveguide are accurately expressed in terms of spherical vector wave functions. Subsequently making use of radial translation of spherical vector wave functions [ 51, [6] the scattering problem is analyzedmorerigorously. A systematicexperimental program was also carried out t o establish every good agreement betweenthetheoretically derived and experimentally measof ured results. The analysis presented holds good for any type aperture antenna.

n(n 1) cos 1Voremn= - , ( k ~ ' p , ~e') ~ (COS m@'$ kR ' Sin

+

1 +7

kR

-

+

m

kR' sin 0' aR'

- [R'Z,(kR')]PHm(COS e')

a

Sin

m@'$,

cos

Inorder to determine ain and bin accurately for aprescribed diameter of the open-ended cylindrical guide excited in the transverse electric (TE, 1) mode, the near fields of the guide are estimated accurately over a hemisphere of radius Ro where Ro-<-OO' using Silver's aperture integration formula [7]. The E , H thus determined was subsequently used to calculate ain, bin appearing in (1) and (2). Analysis of the fields scattered by the dielectric sphere could be considerably simplified withoutintroducinganyapproximationforthe incident field if origin ofthecoordinatesystemforexpressing ' the incident field could be shifted from 0 t o 0. This is made possible by expressing the spherical vector wave function appearingin (1) and (2) about adisplacedorigin 0 (Fig. 1) [SI, [ 6 ] w i t h i n d e x m = 1 , a s

Zi(R, e , @ )=

x

(Ainzoemn

+ BinNOemn)

11. ANALYSIS The geometry of the open-endedwaveguide radiating in the presence of the sphereis shown in Fig. 1. Itis ensured that the (02') the cylindrof center of the sphereis located on the axis ical waveguide. vector wave functionandarefunctions If the center of the aperture (of the open-endedwaveguide) andthe spherical of unprimed coordinates (origin 0) R , 8 , @. The expressions is is located at O ' , the fieldradiated at any arbitrary point for coefficients A U nand Bun are as follows: given by I81

E,.(R', e',

=

x
n

(ainMofemn bi,Noremn)

+

(1) (2)

Z i ( ~ 'e', 4') =+Yo ,
where

x
n

(ai,Noremn

+ binZOfemn)

- [n(n + 1) + u(u + 1)

*

a(m, n, -m, u , p )

Manuscript received July 8, 1981; revised November 30, 1981. This work mas supported by DRDO, Governmentof India. Theauthorsarewith the ElectromagneticsandAntennasGroup, Institute of Technology, Madras Centre for Systems and Devices, Indian 600 036, India.

The n from model offers advantagesi extracting the anisotropy coefficient the Doppler spectrum of the received signal.. Tech. [2] W. vol. Unit vectors associated with (R.1058-1061. 1975. Time Harmonic EM Fields.
I . Lo. VOL.
0018-926X/82/1100-1240$00.
I. has been explained inananisotropicscatteringmodeldevelopedbyBirkemeier e t al. Antennas Propagat. New York: McCraw-Hill. Mason. AnnArbor. no. bdn
[I]
The anisotropic scattering model developed by Birkemeier is based on ascatteringtheory developed byTatarski [4].." IEEE Trans. ch. Bannerjee. Tai.75 1982 IEEE 0
. Whenever disagreement is found in the E-plane. Ho. 69-5.D. ch. Mason.1240
IEEE TRANSACTIONS
ON ANTENNAS AND PROPAGATION. V. V . and K. the edge diffraction was not in the taken account. H . CONCLUSION A more systematic approach to the problem of analysis of radiation patterns of open-ended guides radiating in the presence of a dielectric sphere has been presented. Foster. Electromagnetic Theory. This coefficient can be considered a basic parameter characterizing the state the atof mosphere.POST. no. J. J . [4] H . R . S. Microwave Antenna Theory and Design. May 1971. results.3(b). the error could be attributed to the fact that while calculating the incidentfield. vol.and H-plane patterns measured at a frequency of 9. Free space propagation constant. The measured E. T. IA 50011. Spherical hankel function.'' IEEE Trans. Dec. R. T. F. Harrington. 8.and H-plane amplitude and phase patterns are shown in Figs.
1 The anechoicchamber was built out of ECCOSORB-CVH-NRL Manuscript received October 30.87 GHz. revised March 1." fEEE Trans. is This effect.
assembly was mountedonanazimuthpositionerinside an anechoic chamber' such that the axis of rotation of the posiwere tioner passed through 0. in the form power versus of Doppler frequency or power versus cross-path position. New York: Dover. G . R . Sratton. 6.1982. "Radiation characteristics of a dielectricsphere-loadedcorrugatedpipe. REFERENCES
V . 5. pp. "Multiple scattering by spheres. 1969. Microwave Theory Tech.1981. into which is somewhat significant E-plane. Efforts to evaluate theanisotropycoefficientfromRake forwardscatterradar signals using Birkemeier's modelare complicated by the fact that data. pp. [3] P." IEEE Trans. pp. Urbana. Chatterjee. Ramanujam. AP-23. 3(c). and C.. absorbers and was used previously to measure the patterns of a number The authors are with theDepartment of Electrical Engineering. and M. "Radiation from a homogeneous spheremounted on a waveguide aperture. Electric amplitude field coefficients the for scattered field located outside the sphere. [2]. Rep. NOMENCLATURE Spherical polar coordinates of a point in space. The validity of the analysis has been supported by measured results based on asystematicexperimentalstudy. J . 1975. APSO. S ." Ph. 3(a). 6 . Associated legendre polynomial of first kind. the half-power width of the Doppler spectrum can fluctuate a great deal. Crosswell. NOVEMBER 1982 designusingdielectric lenses. Sept.pp. A. Free space admittance. Thesimplifiedanisotropic in t i communication hs permits scattering model described simple. J . 1941. Incident electric field amplitude coefficients. Hagan. 647-656. 7. Much of this variability is caused by winds in the scattering volume. Sept. DEVELOPMENT OF THE MODEL I
z:( k d ) k
adn. dissertation. . This Gaussian scattering model is mcan to be used for interpretingthe Doppler spectraof signals taken from a forwardscatterradarsystemequippedwitha Rake receiver. Ames. Neelakantaswamy and D. 1975. ACKNOWLEDGMENT The authors are thankful to P. AP-23." Antenna University Lab. butwith A as aparameter [ 5 ] . IV. The calculated results show satisfactory agreement with the measured results. 378-390. vol.."Microwaveirradiation
[5]
[6]
[7] [8] [9]
\
?
A Simplified Model for Interpreting the Doppler Spectrum of Forward-Scatter Radar Signals
ROBERT E. B. NO. However.waveguideradiatingin the presence of the sphere) was 92 cm. Antennas Propugat. AND HOSNY M. K . Silver. 1972. 3(d) forR = 92 cm. Relative permittivity of the dielectric. Electric amplitude field coefficients the for fields located inside the sphere. "Multiple scattering of EM waves by spheres-Pan IMultipoleexpansion andray opticalsolution.. The distance of separation between transmitter (source the horn antenna) and receiver (test) antenna (viz. even after the effect of the wind has been taken into account. Iowa of feed horns at X-band with very successful and repeatable measured State University. 728-730. 1965. B. 4). New York: McCraw-Hill Book Co. of Illinois.1961. MTT-23. The anisotropy in the scatteringmodelaccounts diffor the differences in the correlation lengths along the ferent axes. INTRODUCTION
Records of the Doppler frequency of signals received by a Rake forward scatter radar sounding system indicate considerable variability in the shape of the Doppler spectra. F. The study reported here is expected to be of value in a number of applications. "The electromagnetic radiationfromsimplesources inthe presence of a homogeneousdielectricsphere. vol. Univ. Prithviraj. IEEE. Michigan. S . Bruning and Y.The analysis could beemployed any for type of aperture antenna including flared horns. which evidence of fluctuations in the azimuthal angle dependence of the scattered signal. IBRAHIM
Absrrucr-An approximate form of Birkemeier's anisotropic scattering function is developed. must be fit to a family of theoretical curves using the samevariables. Antennas Propagat. S. 5 . direct evaluationof the anisotropy coefficient. The E. In Birkemeier's model the ratio of the horizontal correlation distance to the vertical correlation distance is defined as the anisotropy coefficient A . AP-19. Govind of our group for their interest in our work and their assistance in the experimental work. SENIOR MEMBER.